Probability with a Deck of Cards
When you work with a standard deck of cards, probability is usually found with
probability = favorable outcomes / total outcomes
A standard deck has 52 cards. It helps to remember the structure:
- 4 suits: hearts, diamonds, clubs, spades
- 13 cards in each suit
- 2 colors: red and black
- face cards: jack, queen, king
Method
- Identify the event
Read carefully what card or group of cards is being described.
- Count the favorable cards
Find how many cards match the condition. Use the deck structure to count accurately.
- Count the total possible cards
For a single-draw problem, this is usually 52.
- Form the fraction
Write favorable over total.
- Simplify the answer
Reduce the fraction to lowest terms if possible.
Example counting ideas
- A specific rank, such as kings: 4 cards
- A suit, such as hearts: 13 cards
- Red cards: 26 cards
- Face cards: 12 cards
Check your work
Make sure your fraction is between 0 and 1. If your answer seems larger than 1 or does not match the number of matching cards, recount the favorable outcomes.